We presented the results of an experiment where the microwave-induced transitions between the ground and first-excited Rydberg states are observed for the first time for the surface electrons on superfluid helium confined in a micron-size channel with dimensions much less than the radiation wavelength. To observe the resonance signal from a few thousand of electrons, we employed a conductive-detection method by observing a change in the electron current through the channel in response to the resonant heating of SE by the microwave absorption. The observed large broadening of the resonance line on the order of 10 GHz is due to the inhomogeneous distribution of the pressing electric field acting on SE and is in a reasonable agreement with our numerical calculations. It seems to be feasible to significantly reduce this broadening by decreasing the width of the electron system in the channel. In particular, it has been already demonstrated that such width can be reduced to effectively a single electron across the channel [1]}, [2]}. At the same time, the reduction of the total number of SE in the channel would require development of an ultra-sensitive detection method. Such an ultra-sensitive method can be based on the image-charge detection demonstrated earlier, providing further improvements in the detection circuit are developed [3]}. The experiment described here was motivated by the potential realization of the spin-orbit coupling in SE and detection of the spin states of electrons, thus can be considered as a first step towards the spin qubits on liquid helium.
